# Solution. Because you are not doing business in the state of New York, you only need to do the calculations at the end of each policy year.

Save this PDF as:

Size: px
Start display at page:

Download "Solution. Because you are not doing business in the state of New York, you only need to do the calculations at the end of each policy year."

## Transcription

1 Exercises in life and annuity valuation. You are the valuation actuary for the Hard Knocks Life Insurance Company offering life annuities and life insurance to guinea pigs. The valuation interest rate is 2%, and mortality of guinea pigs follows De Moivre s Law with l x = 4 x, 0 x 4. You can assume that times after age 4 are ignored. Your company issues fixed deferred annuities to guinea pigs. The interest rate is guaranteed at 3% for the first two years, and % thereafter. The surrender charge is 0% the first year, 5% the second year, and 0% thereafter. Calculate the reserve for a \$000 single premium deferred annuity at issue sold to a newborn. There are no front-end loads. Assume that you use Commissioners Annuity Reserve Valuation Method and you are not doing this in the state of New York. Regulations require that surplus must be 3% of assets at the policy issue date. Find the additional surplus investment requirement for this policy. A. 5 B. 47 C. 44 D. 4 E. 38 Because you are not doing business in the state of New York, you only need to do the calculations at the end of each policy year. Time Fund Value Cash Surrender Value PV of Cash Value As expected, the reserve is given by the present value of the guaranteed cash value at the end of the second policy year, when the surrender charge wears off, and it equals Without a surplus contribution, the company only has 000 worth of assets, and would not be allowed to issue the policy. If the minimum surplus investment is x, then we must have x = 0.03, x and x = = Answer D. 2. You are the valuation actuary for the Hard Knocks Life Insurance Company offering life annuities and life insurance to guinea pigs. The valuation interest rate is 2%, and mortality of guinea pigs follows De Moivre s Law with l x = 4 x, 0 x 4. You can assume that times after age 4 are ignored. Your company issues fixed deferred annuities to guinea pigs. The interest rate is guaranteed at 3% for the first two years, and %

2 thereafter. The surrender charge is 0% the first year, 5% the second year, and 0% thereafter. Calculate the reserve for a \$000 single premium deferred annuity at issue sold to a newborn. There are no front-end loads. You are using the Commissioners Annuity Reserve Valuation Method the state of New York. Find required surplus investment if the regulators require 3% surplus at issue for this policy. A. 38 B. 4 C. 44 D. 47 E. 5 The state of New York requires CARVM reserves for all possible dates in the applicable future. Here, the significant dates are first days of each policy year, when previous year s surrender charge wears off, and cash value suddenly increases. These are the numbers for first days of policy years: Time Fund Value Cash Surrender Value PV of Cash Value Note that beyond t = 2, the guaranteed accumulation rate is less than the valuation rate, so those times cannot produce greater present value than Thus the initial reserve is If the capital investment is x, then x = 0.03, x so that x = = Answer E. 3. Your company issues a \$,000 fully discrete whole life insurance policy to a population of guinea pigs whose mortality follows De Moivre s Law with l x = 4 x, 0 x 4. Calculate the level benefit premium reserve for such a policy at duration, if issued to a newborn. Assume that the valuation interest rate for this problem is 0%. A. 0 B. 50 C. 00 D. 50 E. 200 Because DeMoivre s Law holds, a newborn guinea pig has a 0.25 probability of dying in each of the years, 2, 3, 4. Thus: A 0 = = (obviously, this is for 0% interest always, because everyone dies eventually),

3 a 0 = = 2.5, 4 Also, P 0 = A 0 a 0 = 2.5 = A = =, a = = 2, 3 and the level premium benefit reserve for this policy is: 000 V 0 = 000A 000P 0 a = = 200. Answer E. 4. Your company issues a \$,000 fully discrete whole life insurance policy to a population of guinea pigs whose mortality follows De Moivre s Law with l x = 4 x, 0 x 4. Calculate the level benefit premium reserve for such a policy at duration, if issued to a newborn. Assume that the valuation interest rate for this problem is 0%. Life insurance regulators allow you to use Full Preliminary Term reserving method for this life insurance policy for guinea pigs. What will be the difference between Full Preliminary Term reserve and Level Benefit Premium reserve at time t = 2? A. 0 B. 50 C. 00 D. 50 E. 200 Because DeMoivre s Law holds, a newborn guinea pig has a 0.25 probability of dying in each of the years, 2, 3, 4. Thus: A 0 = = (obviously, this is for 0% interest always, because everyone dies eventually), a 0 = = 2.5, 4 P 0 = A 0 = a = Under Full Preliminary Term, modified benefit premiums will be: First year: α = A 0: = 4, Renewal: β = A a = 2. We have A 2 =, a 2 = + =.5, and therefore V FPT 0 = 000A 2 000β a 2 = = 250.

4 000 V = 000A 000P a = = 400. The modified reserve is significantly smaller, by \$50. Answer D. 5. Your company issues a \$,000 fully discrete whole life insurance policy to a population of guinea pigs whose mortality follows De Moivre s Law with l x = 4 x, 0 x 4. Assume the 980 National Association of Insurance Commissioners Standard Nonforfeiture Law applies and calculate the minimum surrender cash value required by law for this policy at the end of policy year. Assume that the level benefit premium is used for valuation, and the policy is issued to a newborn. Valuation rate is 0%. A. 52 B. 77 C. 200 D. 233 E. 280 This requires establishing the nonforfeiture premium as prescribed by law. The rule starts with comparison of the benefit premium with Here, level benefit premium is 0.40 (per dollar of benefit), clearly greater than In this case, first year expense allowance for the purpose of nonforfeiture benefits calculation is Note that A 0 = and a 0 = = 2.5. The nonforfeiture renewal premium (per dollar) is: P a = A =.06 a = The nonforfeiture value at time is calculated using basic reserve methodology: CV = 000A 000Pa a = = 52. Answer A. 6. Society of Actuaries Course 50 Sample Examination , Problem No. 30 For a fully discrete whole life insurance of 000 on ( x), you are given: (i) i = (ii) Reserves are determined using a modified reserve method, where the modification period is the entire policy period, the modified premium for each of the first three years is 7.72, and modified premiums are level thereafter. (iii) a x:3 = (iv) a x+3 = (v) 3 E x = (vi) 000A x = (vii) 000A x+20 = Calculate the modified reserve at the end of year 20.

5 We have 000A x = α a x:3 + β 3 a x, so that β = 000A x α a x:3 a = 000A x α a x:3 = 3 x 3E x a x+ 3 The modified reserve sought is V Mod x = 000A x+20 β a x+20 = 000A x+20 β A x+20 i + i Society of Actuaries Course 50 Sample Examination , Problem No. 34 You are given (i) At the beginning of year t At the end of year t Liabilities (reserves) 4,800,000 5,000,000 Surplus,200,000,380,000 (ii) For year t Premium Income 800,000 Investment Income unknown Death Benefits 420,000 Withdrawal Benefits 200,000 Commissions 80,000 Other Expenses 220,000 Increase in Reserves unknown (iii) Premiums, expenses, and commissions are paid at the beginning of the year. (iv) Death benefits and withdrawal benefits are paid at the end of the year. Calculate i, the interest rate earned on assets in year t. A. 5.% B. 5.89% C. 6.46% D. 7.% E. 7.69% Assets at the beginning of the year equal to the sum of liabilities and surplus, i.e., 6,000,000. Similarly, 6,380,000 = Assets at the end of the year, but this also equals 6,000,000 + Premiums Commissions Expenses + Investment Income Death Benefits Withdrawal Benefits = 6,000, ,000 80, ,000 + Investment Income 420, ,000 = = 5,880,000 + Investment Income. Therefore, Investment Income = 500,000. The interest rate earned is 500,000/(6,000,000 + Premiums Commissions Expenses) = = 500,000/6,500,000 = 7.69%. Answer E.

6 8. Society of Actuaries Course 50 Sample Examination , Problem No. 35 For a fully discrete insurance of on ( x), you are given: (i) Reserves are determined using a modified reserve method, where the modification period is the entire policy period, the modified premium for the first year, α, is given by α = α FPT, if β FPT α FPT 0.04, β 0.04, otherwise, and modified premiums, β, are level thereafter. (ii) d = (iii) a x = 3. (iv) a x:0 = (v) A x:0 = (vi) A x: = Calculate β. A B C D E We have α FPT = A x: = 0.006, d a x = = 0.22 = A x = α FPT + β FPT ( a x ) = β FPT, and this results in β FPT = Therefore β FPT α FPT = < 0.04, and full preliminary term applies. Hence, β = β FPT = Answer A. 9. Society of Actuaries Course 50 Sample Examination , Problem No. 36 For a fully discrete insurance of on ( x), you are given: (i) Reserves are determined using a modified reserve method, where the modification period is the entire policy period, the modified premium for the first year, α, is given by α = α FPT, if β FPT α FPT 0.04, β 0.04, otherwise, and modified premiums, β, are level thereafter. (ii) d = 0.06.

7 (iii) a x = 3. (iv) a x:0 = (v) A x:0 = (vi) A x: = Calculate the modified reserve at policy duration 0, 0 V x Mod. A B C D E We have α FPT = A x: = 0.006, d a x = = 0.22 = A x = α FPT + β FPT ( a x ) = β FPT, and this results in β FPT = Therefore β FPT α FPT = < 0.04, and full preliminary term applies. Hence, β = β FPT = 0.24 = Using that value, Mod = A x+0 β a x+0 = d a x+0 β a x+0 = 0 V x = ( ) a x+0 = a x+0. We do not have a x+0 but we can find it from this identity a x = a x:0 + 0 E x a x+0, so that a x+0 = a a x x: = E x Finally, 0V x Mod = a x Answer E. 0. Society of Actuaries Course 50 Sample Examination , Problem No. 5 For a fully discrete whole life insurance of on x ( ), you are given: (i) Cash value is k CV = k V x k SC. (ii) The surrender charge is k SC = P x. (iii) 000P x = 9.55.

8 (iv) 000A x+20 = (v) i = (vi) b k is the amount of paid-up insurance available at time k, determined using the equivalence principle. Calculate 000b 20. A. 254 B. 333 C. 498 D. 578 E. 666 We have 20V x = A x+20 P x a x+20 = A x+20 P x A x+20 = d = Furthermore 20CV = 20 V x 20 SC = Finally 000b 20 = CV A x Answer C.. Society of Actuaries Course 50 Sample Examination , Problem No. 37 For a fully discrete insurance of on ( x), you are given: (i) Reserves are determined using a modified reserve method, where the modification period is the entire policy period, the modified premium for the first year, α, is given by α = α FPT, if β FPT α FPT 0.04, β 0.04, otherwise, and modified premiums, β, are level thereafter. (ii) d = (iii) a x = 3. (iv) a x:0 = (v) A x:0 = (vi) A x: = For a fully discrete 0-year endowment insurance of on ( x), calculate β. A. 0.0 B C D E We have

9 A x:0 = d a x:0 = = Furthermore, α FPT = A x: and so that = 0.006, = A x:0 = α FPT + β FPT ( a x:0 ) = β FPT ( 7.55 ), β FPT = Therefore, β FPT α FPT = > Based on this, for this policy, α = β 0.04, and resulting in = A x:0 = α + β a x:0 β = Answer E. ( ) = β β = 7.55β 0.04, 2. Society of Actuaries Course 50 Sample Examination , Problem No. 37 For a fully discrete insurance of on ( x), you are given: (i) Reserves are determined using a modified reserve method, where the modification period is the entire policy period, the modified premium for the first year, α, is given by α = α FPT, if β FPT α FPT 0.04, β 0.04, otherwise, and modified premiums, β, are level thereafter. (ii) d = (iii) a x = 3. (iv) a x:0 = (v) A x:0 = (vi) A x: = For a fully discrete 0-year endowment insurance of on ( x), calculate the modified reserve at policy duration, V Mod x:0. A. 0 B C D E We have A x:0 = d a x:0 = =

10 Furthermore, α FPT = A x: and so that = 0.006, = A x:0 = α FPT + β FPT ( a x:0 ) = β FPT ( 7.55 ), β FPT = Therefore, β FPT α FPT = > Based on this, for this policy, α = β 0.04, and resulting in = A x:0 = α + β a x:0 β = Therefore ( ) = β β = 7.55β 0.04, V Mod x:0 = α ( + i) q ( β 0.04) x = d A x: d p x A = β 0.04 A x: d A x: x: d = Answer B.

11 o On PV basis, NP covers all benefits, so if premiums commence one second from now, our reserve should be zero! o 5V = 00,000 * A 25+5 NP * ä [25]+5 = * = HW: Reserve at time 0. Answer is Example Mrs. Jackson is a 25 year old that buys a \$00K level premium 0 year term policy. The valuation rate is 4.5%, what is the NLP reserve at time 5? Solution Step : Calc NP o Level premium, so 00,000 * A 25:0 / ä [25]:0 = Step 2: Calc Reserve o 5V = Face * A 25+5:5 NP * ä [25]+5:5 = * = ACE Manuals Page 95

12 Example Mrs. Jackson is a 25 year old that buys a \$00K increasing premium 0 year, 3-pay term policy. The GP starts at \$400 and increases \$00 each year. The valuation rate is 4.5%, what is the NLP reserve at time? Age 000q x p x ä x:5 000 A x :5 ä x :0 000 A x: 0 ä x: A x :5 ä x 000 A x Solution Step : Calculate NP o Note that we now have non-level premiums! A 25:0 / ä [25]:3 will not be enough. o PVFB 0 / PVGP 0 = 00,000 * A 25:0 / (GP + GP 2 * v * p x + GP 3 * v 2 * 2 p x ) = / ( * / * p x *p x+ / ) = 82.39% Step 2: Calculate Reserve o V = 00,000 * A 25+: % * ( * /.045) o A 25+:9 = (A 25:0 - vq x ) / vp x =.0570 o V = o a timeline and note that NP is not level!!! ACE Manuals Page 96

13 mpe [x] = m EA [x]:n / ä [x]:m mea [x]:n = expense allowance m t V [x]:n = A [x]+t:n-t ( m P [x]:n + EA / ä [x]:m ) * ä [x]+t:m-t Example Mr. Ehr is getting married at 25 years of age and he buys a level premium, 5 year, \$00K term policy. What is the modified reserve at time 5 if the total EA = \$00. Age 000q x p x ä x:5 000 A x :5 ä x :0 000 A x: 0 ä x: A x :5 ä x 000 A x Step : Calculate NP o Level premium, so NP = Face * A [25]:5 / ä [25]:5 = /.93 = Step 2: Calculate Reserve without EA o 5V = Face * A 25+5:0 NP * ä [25]+5:0 = * = Step 3: Calculate Modified Reserve (with EA) m t VB [x]:n - m tve [x]:n = (00 /ä [25]:5 ) * ä [25]+5:0 = = 27.7 o Example Mr. Ehr is 25 years of age and he buys a level premium, 5 year, \$00K term policy. What is the CRVM reserve at time 5? ACE Manuals Page 97 AB [25]+:4 = AND ä [25]+:4 = Age 000q x p x äx:5 000 Ax :5 äx :0 000 Ax: 0 äx: Ax :5 ä x:9 000 A x: 9 ä x 000 Ax Solution o EA FPT = ( / ) /.045 = o EA 20pay = ( / ) /.045 = o EA CRVM = min ( , ) = o Since this EA is the same as the prior EA, the reserve will not change!!! o If non-level DB, then take average of DB 2 through DB 0 o If EA < 0 (increasing GPs), then floor it at 0 o Note that EA are not linked to expenses, but they do allow for lower reserves as if expenses were included in the NP calculation

14 Exercise You are the valuation actuary for the Hard Knocks Life Insurance Company offering life annuities and life insurance to guinea pigs. The valuation interest rate is %, and mortality of guinea pigs follows De Moivre s Law with l x = 4 x, 0 x 4. You can assume that times after age 4 are ignored. Your company issues fixed deferred annuities to guinea pigs. The interest rate is guaranteed at 5% for the first two years, and 0% thereafter. The surrender charge is 0% the first year, 5% the second year, and 0% thereafter. Calculate the reserve for a \$000 single premium deferred annuity at issue sold to a newborn. There are no front-end loads. Assume that you use Commissioners Annuity Reserve Valuation Method and you are not doing this in the state of New York. Regulations require that surplus must be 3% of assets at the policy issue date. Find the additional surplus investment requirement for this policy. Because you are not doing business in the state of New York, you only need to do the calculations at the end of each policy year. Time Fund Value Cash Surrender Value PV of Cash Value The reserve is given by the present value of the guaranteed cash value at the end of the third policy year and it equals Without a surplus contribution, the company only has 000 worth of assets, and would not be allowed to issue the policy. If the minimum surplus investment is x, then we must have x = 0.03, x and x =

### Scenario 11+ 23 + 14 3 ( 1011+ 1023 + 1014) = = 1016. 1000 + Answer E.

Exercise. You are the valuation actuary for Glorious Life Insurance Company. You are implementing a new principle-based reserving methodology for your company. You have created a set of 10 economic scenarios

### For educational use by Illinois State University only, do not redistribute - 52 -

The nature of valuation When a life insurance product is created, its premiums are established by the pricing actuary. But a policy that is in force already still requires attention of an actuary in order

### Manual for SOA Exam MLC.

Chapter 6. Benefit premiums. Extract from: Arcones Fall 2010 Edition, available at http://www.actexmadriver.com/ 1/24 Non-level premiums and/or benefits. Let b k be the benefit paid by an insurance company

FLEXIBLE PREMIUM ADJUSTABLE LIFE INSURANCE ACTUARIAL DEMONSTRATION FORM J445 I. DESCRIPTION OF POLICY CHARACTERISTICS This is a flexible premium adjustable life insurance policy under the definitions in

### For educational use by Illinois State University students only, do not redistribute - 71 -

Valuation of life annuities A life annuity is a financial contract in the form of an insurance policy in which a seller (issuer), a life insurance company, makes a series of future payments to a buyer

### Premium Calculation. Lecture: Weeks 12-14. Lecture: Weeks 12-14 (Math 3630) Annuities Fall 2015 - Valdez 1 / 32

Premium Calculation Lecture: Weeks 12-14 Lecture: Weeks 12-14 (Math 3630) Annuities Fall 2015 - Valdez 1 / 32 Preliminaries Preliminaries An insurance policy (life insurance or life annuity) is funded

### WHAT IS LIFE INSURANCE?

UNDERSTANDING LIFE INSURANCE Presented by The Kansas Insurance Department WHAT IS LIFE INSURANCE? a. Insurance Contract issued by an Insurance Company. b. Premiums paid under the contract provide for a

### Valuation Interest Rates

Statutory Valuation and Nonforfeiture Rates A. Life Insurance (s) Valuation Rates Nonforfeiture Rate 10 or less 82 6.75 8.50 83-86 7.25 9.00 87 6.50 8.25 88-93 6.00 7.50 94-98 5.50 7.00 99-02 5.00 6.25

### Asset and Liability Composition in Participating Life Insurance: The Impact on Shortfall Risk and Shareholder Value

Asset and Liability Composition in Participating Life Insurance: The Impact on Shortfall Risk and Shareholder Value 7th Conference in Actuarial Science & Finance on Samos June 1, 2012 Alexander Bohnert1,

### Manual for SOA Exam MLC.

Chapter 6. Benefit premiums Extract from: Arcones Fall 2010 Edition, available at http://www.actexmadriver.com/ 1/90 (#4, Exam M, Spring 2005) For a fully discrete whole life insurance of 100,000 on (35)

### MATH 3630 Actuarial Mathematics I Class Test 2 Wednesday, 17 November 2010 Time Allowed: 1 hour Total Marks: 100 points

MATH 3630 Actuarial Mathematics I Class Test 2 Wednesday, 17 November 2010 Time Allowed: 1 hour Total Marks: 100 points Please write your name and student number at the spaces provided: Name: Student ID:

### STATUTORY CALENDAR YEAR INTEREST RATES BASED ON THE 1980 AMENDMENTS TO THE NAIC STANDARD VALUATION AND NONFORFEITURE LAWS. Valuation Interest Rate

BASED ON THE 1980 AMENDMENTS TO THE NAIC STANDARD VALUATION AND NONFORFEITURE LAWS A. Life Insurance Valuation and Nonforfeiture Rates: (years) Valuation Rate Nonforfeiture Rate1 2006 2006 10 or less 4.50

### 001. Statutory authority. This regulation is promulgated under the authority of NEB. REV. STAT. 44-101.01 and is operative October 1, 2008.

Title 210 - NEBRASKA DEPARTMENT OF INSURANCE Chapter 40 - UNIVERSAL LIFE INSURANCE 001. Statutory authority. This regulation is promulgated under the authority of NEB. REV. STAT. 44-101.01 and is operative

### Article Insurance. (a) (1) In this section the following words have the meanings indicated.

Article Insurance [Previous][Next] 5 306. (a) (1) In this section the following words have the meanings indicated. (2) Change in fund basis means a valuation basis under which the interest rate used to

### 58-58-50. Standard Valuation Law.

58-58-50. Standard Valuation Law. (a) This section shall be known as the Standard Valuation Law. (b) Each year the Commissioner shall value or cause to be valued the reserve liabilities ("reserves") for

### May 2012 Course MLC Examination, Problem No. 1 For a 2-year select and ultimate mortality model, you are given:

Solutions to the May 2012 Course MLC Examination by Krzysztof Ostaszewski, http://www.krzysio.net, krzysio@krzysio.net Copyright 2012 by Krzysztof Ostaszewski All rights reserved. No reproduction in any

### 31A-22-409 Standard Nonforfeiture Law for Individual Deferred Annuities.

31A-22-409 Standard Nonforfeiture Law for Individual Deferred Annuities. (1) This section is known as the "Standard Nonforfeiture Law for Individual Deferred Annuities." (2) This section does not apply

### Termination Values, Minimum Surrender Values and Paid-up Values

Prudential Standard LPS 360 Termination Values, Minimum Surrender Values and Paid-up Values Objective and key requirements of this Prudential Standard This Prudential Standard sets out the requirements

### CHAPTER 45-04-12 VALUATION OF LIFE INSURANCE POLICIES

CHAPTER 45-04-12 VALUATION OF LIFE INSURANCE POLICIES Section 45-04-12-01 Applicability 45-04-12-02 Definitions 45-04-12-03 General Calculation Requirements for Basic Reserves and Premium Deficiency Reserves

Premium Calculation - continued Lecture: Weeks 1-2 Lecture: Weeks 1-2 (STT 456) Premium Calculation Spring 2015 - Valdez 1 / 16 Recall some preliminaries Recall some preliminaries An insurance policy (life

### November 2012 Course MLC Examination, Problem No. 1 For two lives, (80) and (90), with independent future lifetimes, you are given: k p 80+k

Solutions to the November 202 Course MLC Examination by Krzysztof Ostaszewski, http://www.krzysio.net, krzysio@krzysio.net Copyright 202 by Krzysztof Ostaszewski All rights reserved. No reproduction in

### 304.15-315 Standard Nonforfeiture Law for Individual Deferred Annuities. (1) This section shall be known as the "Standard Nonforfeiture Law for

304.15-315 Standard Nonforfeiture Law for Individual Deferred Annuities. (1) This section shall be known as the "Standard Nonforfeiture Law for Individual Deferred Annuities." (2) This section shall not

### [Source: Added at 17 Ok Reg 1659, eff 7-14-00]

TITLE 365. INSURANCE DEPARTMENT CHAPTER 10. LIFE, ACCIDENT AND HEALTH SUBCHAPTER 17. VALUATION OF LIFE INSURANCE POLICIES REGULATION INCLUDING THE INTRODUCTION AND USE OF NEW SELECT MORTALITY FACTORS)

### NORTH CAROLINA GENERAL ASSEMBLY 1981 SESSION CHAPTER 761 SENATE BILL 623

NORTH CAROLINA GENERAL ASSEMBLY 1981 SESSION CHAPTER 761 SENATE BILL 623 AN ACT TO AMEND CHAPTER 58, ARTICLE 22, OF THE GENERAL STATUTES RELATING TO NONFORFEITURE BENEFITS OF LIFE INSURANCE POLICIES AND

### 500.4107 Separate account annual statement and other information to be submitted to commissioner.

THE INSURANCE CODE OF 1956 (EXCERPT) Act 218 of 1956 CHAPTER 41 MODIFIED GUARANTEED ANNUITIES 500.4101 Definitions. Sec. 4101. As used in this chapter: (a) Interest credits means all interest that is credited

### Manual for SOA Exam MLC.

Chapter 5 Life annuities Extract from: Arcones Manual for the SOA Exam MLC Fall 2009 Edition available at http://wwwactexmadrivercom/ 1/94 Due n year temporary annuity Definition 1 A due n year term annuity

### ACTUARIAL GUIDELINE XXXIII DETERMINING CARVM RESERVES FOR ANNUITY CONTRACTS WITH ELECTIVE BENEFITS

ACTUARIAL GUIDELINE XXXIII DETERMINING CARVM RESERVES FOR ANNUITY CONTRACTS WITH ELECTIVE BENEFITS Background Information 1. Introduction The Standard Valuation Law (SVL) defines the methods and assumptions

### VERMONT DEPARTMENT OF BANKING AND INSURANCE REVISED REGULATION 77-2 VERMONT LIFE INSURANCE SOLICITATION REGULATION

VERMONT DEPARTMENT OF BANKING AND INSURANCE REVISED REGULATION 77-2 VERMONT LIFE INSURANCE SOLICITATION REGULATION Section 1. AUTHORITY This rule is adopted and promulgated by the Commissioner of Banking

### Effective 5/10/ A Standard Nonforfeiture Law for Life Insurance.

Effective 5/10/2016 31A-22-408 Standard Nonforfeiture Law for Life Insurance. (1) (a) This section is known as the "Standard Nonforfeiture Law for Life Insurance." (b) This section does not apply to group

### This rule was filed as 13 NMAC 9.7. LIFE INSURANCE AND ANNUITIES UNIVERSAL LIFE INSURANCE

This rule was filed as 13 NMAC 9.7. TITLE 13 CHAPTER 9 PART 7 INSURANCE LIFE INSURANCE AND ANNUITIES UNIVERSAL LIFE INSURANCE 13.9.7.1 ISSUING AGENCY: New Mexico State Corporation Commission [Public Regulation

### 003.05 Net Cash Surrender Value. "Net cash surrender value" means the maximum amount payable to the policyowner upon surrender.

Title 210 - NEBRASKA DEPARTMENT OF INSURANCE Chapter 40 - UNIVERSAL LIFE INSURANCE 001. Statutory authority. This regulation is promulgated under the authority of NEB. REV. STAT. 44-101.01 and is operative

### Manual for SOA Exam MLC.

Chapter 4. Life insurance. Extract from: Arcones Fall 2009 Edition, available at http://www.actexmadriver.com/ (#1, Exam M, Fall 2005) For a special whole life insurance on (x), you are given: (i) Z is

### INSURANCE DEPARTMENT OF THE STATE OF NEW YORK REGULATION NO. 147 (11 NYCRR 98) VALUATION OF LIFE INSURANCE RESERVES

INSURANCE DEPARTMENT OF THE STATE OF NEW YORK REGULATION NO. 147 (11 NYCRR 98) VALUATION OF LIFE INSURANCE RESERVES I, Gregory V. Serio, Superintendent of Insurance of the State of New York, pursuant to

### Be it enacted by the People of the State of Illinois,

AN ACT concerning insurance. Be it enacted by the People of the State of Illinois, represented in the General Assembly: Section 5. The Illinois Insurance Code is amended by changing Sections 223 and 229.2

### RULES OF THE DEPARTMENT OF INSURANCE DIVISION OF INSURANCE CHAPTER 0780-1-40 RELATING TO LIFE INSURANCE SOLICITATION TABLE OF CONTENTS

RULES OF THE DEPARTMENT OF INSURANCE DIVISION OF INSURANCE CHAPTER 0780-1-40 RELATING TO LIFE INSURANCE SOLICITATION TABLE OF CONTENTS 0780-1-40-.01 Purpose 0780-1-40-.05 General Rules 0780-1-40-.02 Scope

### CHAPTER 26.1-34 ANNUITIES

CHAPTER 26.1-34 ANNUITIES 26.1-34-01. Required annuity contract provisions relating to cessation of payment of considerations by contractholder. In the case of annuity contracts issued after June 30, 1979,

### MINIMUM SURRENDER VALUES AND PAID-UP VALUES

MARCH 2002 Actuarial Standard 4.02 MINIMUM SURRENDER VALUES AND PAID-UP VALUES Life Insurance Actuarial Standards Board TABLE OF CONTENTS INTRODUCTION PAGE The Standard 2 Application of the Surrender Value

### IIPRC-LB-04-I-ROP. 3. Rules Repealed, Amended or Suspended by the Rule: None.

IIPRC-LB-04-I-ROP ADDITIONAL STANDARDS FOR INTERMEDIATE PERIOD ENDOWMENT BENEFIT FEATURES FOR INDIVIDUAL LIFE INSURANCE POLICIES (INCLUDING RETURN OF PREMIUM) 1. Date Adopted: March 14, 2009 2. Purpose

### JANUARY 2016 EXAMINATIONS. Life Insurance I

PAPER CODE NO. MATH 273 EXAMINER: Dr. C. Boado-Penas TEL.NO. 44026 DEPARTMENT: Mathematical Sciences JANUARY 2016 EXAMINATIONS Life Insurance I Time allowed: Two and a half hours INSTRUCTIONS TO CANDIDATES:

### Premium Calculation. Lecture: Weeks 12-14. Lecture: Weeks 12-14 (STT 455) Premium Calculation Fall 2014 - Valdez 1 / 31

Premium Calculation Lecture: Weeks 12-14 Lecture: Weeks 12-14 (STT 455) Premium Calculation Fall 2014 - Valdez 1 / 31 Preliminaries Preliminaries An insurance policy (life insurance or life annuity) is

### Manual for SOA Exam MLC.

Chapter 6. Benefit premiums. Extract from: Arcones Fall 2010 Edition, available at http://www.actexmadriver.com/ 1/77 Fully discrete benefit premiums In this section, we will consider the funding of insurance

### ARKANSAS INSURANCE DEPARTMENT LEGAL DIVISION 1200 West Third Street Little Rock, AR 72201-1904 501-371-2820 FAX 501-371-2629

ARKANSAS INSURANCE DEPARTMENT LEGAL DIVISION 1200 West Third Street Little Rock, AR 72201-1904 501-371-2820 FAX 501-371-2629 RULE AND REGULATION NO. 59 MODIFIED GUARANTEED ANNUITIES Table of Contents Section

### 2 Policy Values and Reserves

2 Policy Values and Reserves [Handout to accompany this section: reprint of Life Insurance, from The Encyclopaedia of Actuarial Science, John Wiley, Chichester, 2004.] 2.1 The Life Office s Balance Sheet

### TO: ALL AUTHORIZED LIFE INSURANCE COMPANIES AND FRATERNAL BENEFIT SOCIETIES ATTENTION: CHIEF ACTUARY OR CONSULTING ACTUARY AND CHIEF FINANCIAL OFFICER

November 18, 1982 SUBJECT: INSURANCE WITHDRAWN CIRCULAR LETTER NO. 27 (1982) November 18, 1982 TO: ALL AUTHORIZED LIFE INSURANCE COMPANIES AND FRATERNAL BENEFIT SOCIETIES ATTENTION: CHIEF ACTUARY OR CONSULTING

### Insurance Chapter 482-1-075 ALABAMA DEPARTMENT OF INSURANCE ADMINISTRATIVE CODE

Chapter 482-1-075 ALABAMA DEPARTMENT OF INSURANCE ADMINISTRATIVE CODE CHAPTER 482-1-075 SMOKER NON-SMOKER MORTALITY TABLES FOR USE IN DETERMINING MINIMUM RESERVE LIABILITIES AND NONFORFEITURE BENEFITS

### Life Insurance Buyer s Guide

Page 1 of 5 Life Insurance Buyer s Guide Illinois This guide can show you how to save money when you shop for life insurance. It helps you to: Decide how much life insurance you should buy, Decide what

### BULLETIN NO. 06-21 MAXIMUM RESERVE VALUATION AND NONFORFEITURE RATES

BULLETIN NO. 06-21 TO: FROM: SUBJECT: ALL DOMESTIC LIFE INSURANCE COMPANIES AND CHARITABLE ANNUITIES STEVEN M. GOLDMAN, COMMISSIONER MAXIMUM RESERVE VALUATION AND NONFORFEITURE RATES In accordance with

### Pricing exercise based on a collection of actuarial assumptions Assumptions generally divided into two sets

Whole Life Pricing Pricing exercise based on a collection of actuarial assumptions Assumptions generally divided into two sets Company specific: Mortality, Lapsation, Expenses, Dividends, etc. Prescription

### Life Insurance Buyer s Guide

United of Omaha Life Insurance Company Life Insurance Buyer s Guide Prepared by the National Association of Insurance Commissioners The National Association of Insurance Commissioners is an association

### CHAPTER 45-04-06 SMOKER/NONSMOKER MORTALITY TABLES

CHAPTER 45-04-06 SMOKER/NONSMOKER MORTALITY TABLES Section 45-04-06-01 45-04-06-02 45-04-06-03 45-04-06-04 45-04-06-05 Definitions Alternate Tables Conditions Separability Effective Date 45-04-06-01. Definitions.

### State of New Jersey DEPARTMENT OF BANKING AND INSURANCE PO BOX 325 TRENTON, NJ 08625-0325

CHRIS CHRISTIE Governor KIM GUADAGNO Lt. Governor State of New Jersey DEPARTMENT OF BANKING AND INSURANCE PO BOX 325 TRENTON, NJ 08625-0325 TEL (609) 292-7272 THOMAS B. CONSIDINE Commissioner BULLETIN

### CHAPTER 45-04-05 UNIVERSAL LIFE INSURANCE

CHAPTER 45-04-05 UNIVERSAL LIFE INSURANCE Section 45-04-05-01 De nitions 45-04-05-02 Scope 45-04-05-03 Valuation 45-04-05-04 Nonforfeiture 45-04-05-05 Mandatory Policy Provisions 45-04-05-06 Disclosure

### State of New Jersey DEPARTMENT OF BANKING AND INSURANCE OFFICE OF THE COMMISSIONER PO BOX 325 TRENTON, NJ 08625-0325

CHRIS CHRISTIE Governor KIM GUADAGNO Lt. Governor State of New Jersey DEPARTMENT OF BANKING AND INSURANCE OFFICE OF THE COMMISSIONER PO BOX 325 TRENTON, NJ 08625-0325 TEL (609) 292-7272 KENNETH E. KOBYLOWSKI

### State of New Jersey DEPARTMENT OF BANKING AND INSURANCE OFFICE OF THE COMMISSIONER PO BOX 325 TRENTON, NJ 08625-0325

CHRIS CHRISTIE Governor KIM GUADAGNO Lt. Governor State of New Jersey DEPARTMENT OF BANKING AND INSURANCE OFFICE OF THE COMMISSIONER PO BOX 325 TRENTON, NJ 08625-0325 TEL (609) 292-7272 KENNETH E. KOBYLOWSKI

### Premium calculation. summer semester 2013/2014. Technical University of Ostrava Faculty of Economics department of Finance

Technical University of Ostrava Faculty of Economics department of Finance summer semester 2013/2014 Content 1 Fundamentals Insurer s expenses 2 Equivalence principles Calculation principles 3 Equivalence

### VALUATION OF LIFE INSURANCE POLICIES MODEL REGULATION (Including the Introduction and Use of New Select Mortality Factors)

Table of Contents Model Regulation Service October 2009 VALUATION OF LIFE INSURANCE POLICIES MODEL REGULATION (Including the Introduction and Use of New Select Mortality Factors) Section 1. Section 2.

### Life Insurance Buyer s Guide

Life Insurance Buyer s Guide This guide can show you how to save money when you shop for life insurance. It helps you to: - Decide how much life insurance you should buy, - Decide what kind of life insurance

### Amendment Proposal for. AG 33 Modifications for Non-Elective Incidence Rates. Adopted by the Life Actuarial (A) Task Force, Sept.

Amendment Proposal for AG 33 Modifications for Non-Elective Incidence Rates Adopted by the Life Actuarial (A) Task Force, Sept. 17, 2015 Note: This exposure covers only the language, in Paragraph 2, Elective

### This rule was filed as 13 NMAC 9.3. LIFE INSURANCE AND ANNUITIES VARIABLE ANNUITY CONTRACTS

This rule was filed as 13 NMAC 9.3. TITLE 13 CHAPTER 9 PART 3 INSURANCE LIFE INSURANCE AND ANNUITIES VARIABLE ANNUITY CONTRACTS 13.9.3.1 ISSUING AGENCY: New Mexico State Corporation Commission [Public

### SECONDARY GUARANTEES FOR UNIT LINKED LIFE INSURANCE THE NEED, FEATURES AND RESERVING

SECONDARY GUARANTEES FOR UNIT LINKED LIFE INSURANCE THE NEED, FEATURES AND RESERVING By Irvinder Singh Kohli, Rajneet Kaur, Ritu Behl & Ankur Goel ABSTRACT This paper introduces ULIP products and talks

### TABLE OF CONTENTS. GENERAL AND HISTORICAL PREFACE iii SIXTH EDITION PREFACE v PART ONE: REVIEW AND BACKGROUND MATERIAL

TABLE OF CONTENTS GENERAL AND HISTORICAL PREFACE iii SIXTH EDITION PREFACE v PART ONE: REVIEW AND BACKGROUND MATERIAL CHAPTER ONE: REVIEW OF INTEREST THEORY 3 1.1 Interest Measures 3 1.2 Level Annuity

### Derivation of the IFRS 4 Statement of Comprehensive Income for Insurance Contracts

Derivation of the IFRS 4 Statement of Comprehensive Income for Insurance Contracts The purpose of this document is to specify the creation of the proposed IFRS 4 Statement of Comprehensive Income for Insurance

### NATIONAL INSURANCE COMMISSION GUIDELINES ON APPLICATIONS FOR APPROVAL OF NEW AND REPACKAGED LIFE INSURANCE PRODUCTS

NATIONAL INSURANCE COMMISSION GUIDELINES ON APPLICATIONS FOR APPROVAL OF NEW AND REPACKAGED LIFE INSURANCE PRODUCTS 1.0 INTRODUCTION In a bid to protect policyholders, section 45 of Insurance Act, 2006

### Solution. Let us write s for the policy year. Then the mortality rate during year s is q 30+s 1. q 30+s 1

Solutions to the May 213 Course MLC Examination by Krzysztof Ostaszewski, http://wwwkrzysionet, krzysio@krzysionet Copyright 213 by Krzysztof Ostaszewski All rights reserved No reproduction in any form

### MINNESOTA REQUIREMENTS, DEFERRED INDEXED ANNUITIES

Edition: 11/2010 MINNESOTA REQUIREMENTS, DEFERRED INDEXED ANNUITIES I. Minnesota Specific Requirements The following are the requirements that the department analysts will be applying to deferred indexed

### MINNESOTA REQUIREMENTS, LIFE INSURANCE VARIABLE

Edition: 09/2010 MINNESOTA REQUIREMENTS, LIFE INSURANCE VARIABLE I. Minnesota Specific Requirements to be Included in Life Insurance Policies The following are the requirements that the department analysts

### Buyer s Guide for Deferred Annuities Variable

Buyer s Guide for Deferred Annuities Variable Prepared by the NAIC National Association of Insurance Commissioners This guide does not endorse any company or policy Reprinted by John Hancock Life Insurance

### State of Rhode Island and Providence Plantations DEPARTMENT OF BUSINESS REGULATION Division of Insurance 233 Richmond Street Providence, RI 02903

State of Rhode Island and Providence Plantations DEPARTMENT OF BUSINESS REGULATION Division of Insurance 233 Richmond Street Providence, RI 02903 INSURANCE REGULATION 85 MODIFIED GUARANTEED ANNUITIES Table

### GUIDELINES RELATIVE TO PRODUCTS APPROVAL

Annex E GUIDELINES RELATIVE TO PRODUCTS APPROVAL I. Policy Provisions 1. Suicide The text of Suicide Provision as provided in Circular Letter 14-93CL re Standard Life Insurance Provisions shall be revised

### NAIC Buyer s Guide for Deferred Annuities

NAIC Buyer s Guide for Deferred Annuities Prepared by the National Association of Insurance Commissioners The National Association of Insurance Commissioners is an association of state insurance regulatory

### Individual Fixed Premium Deferred Variable Annuity Contract Standards (with Separate and General Accounts)

Individual Fixed Premium Deferred Variable Annuity Contract Standards (with Separate and General Accounts) 1. Date Adopted: September 28, 2007 2. Purpose and Scope: The purpose of this rule is to establish

### Manual for SOA Exam MLC.

Chapter 5 Life annuities Extract from: Arcones Manual for the SOA Exam MLC Fall 2009 Edition available at http://wwwactexmadrivercom/ 1/70 Due n year deferred annuity Definition 1 A due n year deferred

Buyer s Guide for Deferred Annuities Table of Contents What Is an Annuity?... 1 When Annuities Start to Make Income Payments... 1 How Deferred Annuities Are Alike... 1 How Deferred Annuities Are Different...

### MODEL VARIABLE ANNUITY REGULATION. Qualifications of Insurance Companies to Issue Variable Annuities

MODEL VARIABLE ANNUITY REGULATION Table of Contents Section 1. Section 2. Section 3. Section 4. Section 5. Section 6. Section 7. Section 8. Section 9. Section 10. Authority Definitions Qualifications of

### VARIABLE ANNUITY CONTRACTS

RULE AND REGULATION 6 Agency # 054.00 VARIABLE ANNUITY CONTRACTS *Provisions of this rule and regulation as it pertains to variable life insurance have been superseded by Rule and Regulation 33. See Article

### CHAPTER 166. AN ACT to create 206.181 and 206.201 of the statutes, relating to nonforfeiture values of life insurance policies and valuation thereof.

204 LAWS OF WISCONSIN-CR. 166 of deceased members. Such pension shall not exceed one-half the salary of such officer at the time of his pensioning or death. Approved May 19, 1943. No. 214, S.] [Published

### Life Insurance Reserves -- Proposed AG VACARVM and Life PBR. The purpose of this notice is to alert life insurance companies to federal

Part III -- Administrative, Procedural, and Miscellaneous Life Insurance Reserves -- Proposed AG VACARVM and Life PBR Notice 2008-18 SECTION 1. PURPOSE The purpose of this notice is to alert life insurance

### Buyer s Guide for. Deferred Annuities

Buyer s Guide for Deferred Annuities Prepared by the NAIC National Association of Insurance Commissioners The National Association of Insurance Commissioners is an association of state insurance regulatory

### Title 24-A: MAINE INSURANCE CODE

Maine Revised Statutes Title 24-A: MAINE INSURANCE CODE Chapter 11: ASSETS AND LIABILITIES 953-A. APPLICABLE INTEREST RATES 1. The interest rates used in determining the minimum standard for the valuation

### SECTION 99.1 Purposes. The purposes of this Part are:

INSURANCE DEPARTMENT OF THE STATE OF NEW YORK REGULATION NO. 151 (11 NYCRR 99) VALUATION OF ANNUITY, SINGLE PREMIUM LIFE INSURANCE, GUARANTEED INTEREST CONTRACT AND OTHER DEPOSIT RESERVES I, Neil D. Levin,

### GLOSSARY. A contract that provides for periodic payments to an annuitant for a specified period of time, often until the annuitant s death.

The glossary contains explanations of certain terms and definitions used in this prospectus in connection with the Group and its business. The terms and their meanings may not correspond to standard industry

### LEVELING THE NET SINGLE PREMIUM. - Review the assumptions used in calculating the net single premium.

LEVELING THE NET SINGLE PREMIUM CHAPTER OBJECTIVES - Review the assumptions used in calculating the net single premium. - Describe what is meant by the present value of future benefits. - Explain the mathematics

### NEW JERSEY FORM REQUIREMENTS INDIVIDUAL GENERAL ACCOUNT ANNUITIES

INDIVIDUAL GENERAL ACCOUNT ANNUITIES The same contract form shall not be issued as both an immediate and a deferred annuity. An annuity form shall not be identified as a single premium contract if it contains

### (125th General Assembly) (Substitute House Bill Number 243) AN ACT

(125th General Assembly) (Substitute House Bill Number 243) AN ACT To amend sections 3901.043, 3901.51, 3905.24, and 3915.073, to enact section 3905.422, and to repeal sections 3957.01, 3957.02, 3957.03,

### Life Insurance Valuation Interest Rate

Life Insurance Valuation Interest Rate Scott Gibson, FSA, MAAA Actuaries and Consultants (972) 850-0850 SGibson@LewisEllis.com Important Facts About the Standard Valuation and Standard Nonforfeiture Laws

### Mr. Wan Feng Executive Director, Vice President May 2007, Nan Ning

The distinctive characteristics of life insurance operation Mr. Wan Feng Executive Director, Vice President May 2007, Nan Ning Foreword The characteristics Why we need to understand them How we analyze

### INSTITUTE AND FACULTY OF ACTUARIES EXAMINATION

INSTITUTE AND FACULTY OF ACTUARIES EXAMINATION 27 April 2015 (pm) Subject CT5 Contingencies Core Technical Time allowed: Three hours INSTRUCTIONS TO THE CANDIDATE 1. Enter all the candidate and examination

### Buyer s Guide for. Deferred Annuities. For personal, non-commercial use only.

Buyer s Guide for Deferred Annuities Prepared by the NAIC National Association of Insurance Commissioners The National Association of Insurance Commissioners is an association of state insurance regulatory

### Universal Life Insurance

Universal Life Insurance Lecture: Weeks 11-12 Thanks to my friend J. Dhaene, KU Leuven, for ideas here drawn from his notes. Lecture: Weeks 11-12 (STT 456) Universal Life Insurance Spring 2015 - Valdez

### THE CONSTRUCTION OF A SURVIVORSHIP LIFE INSURANCE POLICY

THE CONSTRUCTION OF A SURVIVORSHIP LIFE INSURANCE POLICY PERTINENT INFORMATION Mr. and Mrs. Kugler are considering \$1,000,000 of life insurance to provide estate liquidity at the survivor s death to cover

### The Hartford Saver Solution SM A FIXED INDEX ANNUITY DISCLOSURE STATEMENT

The Hartford Saver Solution SM A FIXED INDEX ANNUITY DISCLOSURE STATEMENT THE HARTFORD SAVER SOLUTION SM FIXED INDEX ANNUITY DISCLOSURE STATEMENT This Disclosure Statement provides important information

### FG Guarantee-Platinum. A Single Premium, Fixed Deferred Annuity with tax-deferred earnings featuring a choice of a 3, 5 or 7-year rate guarantee

A Single Premium, Fixed Deferred Annuity with tax-deferred earnings featuring a choice of a 3, 5 or 7-year rate guarantee ADV 1010 (01-2011) Fidelity & Guaranty Life Insurance Company Rev. 07-2014 12-716

### SOCIETY OF ACTUARIES. EXAM MLC Models for Life Contingencies EXAM MLC SAMPLE QUESTIONS

SOCIETY OF ACTUARIES EXAM MLC Models for Life Contingencies EXAM MLC SAMPLE QUESTIONS The following questions or solutions have been modified since this document was prepared to use with the syllabus effective

### Ch. 87 SPECIAL REQUIREMENTS 31 CHAPTER 87. REQUIREMENTS FOR CERTAIN LIFE INSURANCE POLICIES AND SALES PRACTICES GENERAL PROVISIONS

Ch. 87 SPECIAL REQUIREMENTS 31 CHAPTER 87. REQUIREMENTS FOR CERTAIN LIFE INSURANCE POLICIES AND SALES PRACTICES GENERAL PROVISIONS Sec. 87.1. Definitions. 87.2. Purpose. 87.3. Guaranteed annual endowments.

### CHAPTER 16 REPLACEMENT OF LIFE INSURANCE AND ANNUITIES [Prior to 10/22/86, Insurance Department[510]]

Insurance[191] Ch 16, p.1 CHAPTER 16 REPLACEMENT OF LIFE INSURANCE AND ANNUITIES [Prior to 10/22/86, Insurance Department[510]] 191 16.1(507B) Purpose and authority. 16.1(1) The purpose of these rules

Buyer s Guide for Deferred Annuities Fixed Table of Contents What Is an Annuity?...2 When Annuities Start to Make Income Payments... 2 How Deferred Annuities Are Alike... 2 How Deferred Annuities Are Different...

### 304.6-145 Minimum standards -- Operative dates. (1) The interest rates used in determining the minimum standard for the valuation of: (a) All life

304.6-145 Minimum standards -- Operative dates. (1) The interest rates used in determining the minimum standard for the valuation of: (a) All life insurance policies issued in a particular calendar year,

### ACTS 4301 FORMULA SUMMARY Lesson 1: Probability Review. Name f(x) F (x) E[X] Var(X) Name f(x) E[X] Var(X) p x (1 p) m x mp mp(1 p)

ACTS 431 FORMULA SUMMARY Lesson 1: Probability Review 1. VarX)= E[X 2 ]- E[X] 2 2. V arax + by ) = a 2 V arx) + 2abCovX, Y ) + b 2 V ary ) 3. V ar X) = V arx) n 4. E X [X] = E Y [E X [X Y ]] Double expectation